Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 14 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.If 9 kites cost ₹126, how much do 3 kites cost? (a) ₹56 (b) ₹378 (c) ₹42 (d) ₹120
2. 2.If 9 pens cost ₹180, how much do 8 pens cost? (a) ₹179 (b) ₹180 (c) ₹160 (d) ₹1440
3. 3.If 6 kites cost ₹84, how much do 7 kites cost? (a) ₹98 (b) ₹112 (c) ₹85 (d) ₹588
4. 4.₹135 is shared between two friends in the ratio 2 : 7. How much is the bigger share? (a) ₹15 (b) ₹30 (c) ₹120 (d) ₹105
5. 5.If 4 kites cost ₹48, how much do 12 kites cost? (a) ₹56 (b) ₹156 (c) ₹576 (d) ₹144
6. 6.6 workers can build a wall in 13 days. How many days will 2 workers take, working at the same speed? (a) 40 days (b) 9 days (c) 39 days (d) 17 days
7. 7.9 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 26 days (b) 13 days (c) 28 days (d) 27 days
8. 8.₹182 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹112 (b) ₹14 (c) ₹91 (d) ₹70
9. 9.5 workers can build a wall in 7 days. How many days will 7 workers take, working at the same speed? (a) 5 days (b) 6 days (c) 4 days (d) 9 days
10. 10.If 5 pens cost ₹45, how much do 11 pens cost? (a) ₹495 (b) ₹99 (c) ₹108 (d) ₹51
11. 11.₹273 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹105 (b) ₹168 (c) ₹21 (d) ₹189
12. 12.₹210 is shared between two friends in the ratio 1 : 6. How much is the bigger share? (a) ₹30 (b) ₹105 (c) ₹180 (d) ₹210
13. 13.5 workers can build a wall in 4 days. How many days will 2 workers take, working at the same speed? (a) 10 days (b) 11 days (c) 7 days (d) 1 day
14. 14.5 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 13 days (b) 5 days (c) 4 days (d) 6 days
15. 15.₹132 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹48 (b) ₹84 (c) ₹66 (d) ₹12
16. 16.₹100 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹10 (b) ₹70 (c) ₹50 (d) ₹30
17. 17.₹111 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹111 (b) ₹74 (c) ₹37 (d) ₹75
18. 18.If 2 mangoes cost ₹16, how much do 11 mangoes cost? (a) ₹96 (b) ₹88 (c) ₹25 (d) ₹176
19. 19.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹170 (b) ₹34 (c) ₹153 (d) ₹17
20. 20.₹336 is shared between two friends in the ratio 5 : 7. How much is the bigger share? (a) ₹168 (b) ₹140 (c) ₹196 (d) ₹28
21. 21.If 3 pens cost ₹39, how much do 4 pens cost? (a) ₹65 (b) ₹40 (c) ₹52 (d) ₹156
22. 22.If 2 kites cost ₹12, how much do 9 kites cost? (a) ₹108 (b) ₹19 (c) ₹60 (d) ₹54
23. 23.If 5 mangoes cost ₹110, how much do 3 mangoes cost? (a) ₹88 (b) ₹66 (c) ₹108 (d) ₹330
24. 24.If 9 notebooks cost ₹54, how much do 12 notebooks cost? (a) ₹78 (b) ₹57 (c) ₹648 (d) ₹72
25. 25.3 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 9 days (b) 11 days (c) 16 days (d) 15 days
26. 26.₹160 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹80 (b) ₹16 (c) ₹48 (d) ₹112
27. 27.If 4 notebooks cost ₹80, how much do 5 notebooks cost? (a) ₹120 (b) ₹100 (c) ₹400 (d) ₹81
28. 28.If 9 kites cost ₹108, how much do 3 kites cost? (a) ₹102 (b) ₹48 (c) ₹36 (d) ₹324
29. 29.If 6 pens cost ₹138, how much do 9 pens cost? (a) ₹1242 (b) ₹141 (c) ₹230 (d) ₹207
30. 30.4 workers can build a wall in 14 days. How many days will 2 workers take, working at the same speed? (a) 16 days (b) 7 days (c) 12 days (d) 28 days
31. 31.₹286 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹104 (b) ₹26 (c) ₹143 (d) ₹182
32. 32.₹42 is shared between two friends in the ratio 2 : 5. How much is the bigger share? (a) ₹30 (b) ₹12 (c) ₹21 (d) ₹6
33. 33.₹56 is shared between two friends in the ratio 1 : 3. How much is the bigger share? (a) ₹28 (b) ₹14 (c) ₹56 (d) ₹42
34. 34.If 9 kites cost ₹45, how much do 6 kites cost? (a) ₹35 (b) ₹30 (c) ₹42 (d) ₹270
35. 35.If 4 mangoes cost ₹68, how much do 5 mangoes cost? (a) ₹102 (b) ₹85 (c) ₹69 (d) ₹340
36. 36.4 workers can build a wall in 4 days. How many days will 8 workers take, working at the same speed? (a) 3 days (b) 8 days (c) 2 days (d) 1 day
37. 37.If 3 mangoes cost ₹12, how much do 12 mangoes cost? (a) ₹48 (b) ₹21 (c) ₹52 (d) ₹144
38. 38.8 workers can build a wall in 6 days. How many days will 2 workers take, working at the same speed? (a) 25 days (b) 23 days (c) 12 days (d) 24 days
39. 39.₹270 is shared between two friends in the ratio 3 : 7. How much is the bigger share? (a) ₹27 (b) ₹189 (c) ₹81 (d) ₹135
40. 40.If 7 notebooks cost ₹49, how much do 9 notebooks cost? (a) ₹51 (b) ₹441 (c) ₹70 (d) ₹63

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